@misc{HillerKrumkeSalibaetal., author = {Hiller, Benjamin and Krumke, Sven and Saliba, Sleman and Tuchscherer, Andreas}, title = {Randomized Online Algorithms for Dynamic Multi-Period Routing Problems}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-11132}, number = {09-03}, abstract = {The Dynamic Multi-Period Routing Problem DMPRP introduced by Angelelli et al. gives a model for a two-stage online-offline routing problem. At the beginning of each time period a set of customers becomes known. The customers need to be served either in the current time period or in the following. Postponed customers have to be served in the next time period. The decision whether to postpone a customer has to be done online. At the end of each time period, an optimal tour for the customers assigned to this period has to be computed and this computation can be done offline. The objective of the problem is to minimize the distance traveled over all planning periods assuming optimal routes for the customers selected in each period. We provide the first randomized online algorithms for the DMPRP which beat the known lower bounds for deterministic algorithms. For the special case of two planning periods we provide lower bounds on the competitive ratio of any randomized online algorithm against the oblivious adversary. We identify a randomized algorithm that achieves the optimal competitive ratio of \$\frac{1+\sqrt{2}}{2}\$ for two time periods on the real line. For three time periods, we give a randomized algorithm that is strictly better than any deterministic algorithm.}, language = {en} } @misc{HillerVredeveld, author = {Hiller, Benjamin and Vredeveld, Tjark}, title = {On the optimality of Least Recently Used}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10928}, number = {08-39}, abstract = {It is well known that competitive analysis yields too pessimistic results when applied to the paging problem and it also cannot make a distinction between many paging strategies. Many deterministic paging algorithms achieve the same competitive ratio, ranging from inefficient strategies as flush-when-full to the good performing least-recently-used (LRU). In this paper, we study this fundamental online problem from the viewpoint of stochastic dominance. We show that when sequences are drawn from distributions modelling locality of reference, LRU is stochastically better than any other online paging algorithm.}, language = {en} } @misc{HillerVredeveld, author = {Hiller, Benjamin and Vredeveld, Tjark}, title = {Probabilistic analysis of Online Bin Coloring algorithms via Stochastic Comparison}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10726}, number = {08-18}, abstract = {This paper proposes a new method for probabilistic analysis of online algorithms that is based on the notion of stochastic dominance. We develop the method for the Online Bin Coloring problem introduced by Krumke et al. Using methods for the stochastic comparison of Markov chains we establish the strong result that the performance of the online algorithm GreedyFit is stochastically dominated by the performance of the algorithm OneBin for any number of items processed. This result gives a more realistic picture than competitive analysis and explains the behavior observed in simulations.}, language = {en} } @misc{GroetschelHillerTuchscherer, author = {Gr{\"o}tschel, Martin and Hiller, Benjamin and Tuchscherer, Andreas}, title = {Combinatorial Online Optimization: Elevators \& Yellow Angels}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-10360}, number = {07-36}, abstract = {In \emph{classical optimization} it is assumed that full information about the problem to be solved is given. This, in particular, includes that all data are at hand. The real world may not be so nice'' to optimizers. Some problem constraints may not be known, the data may be corrupted, or some data may not be available at the moments when decisions have to be made. The last issue is the subject of \emph{online optimization} which will be addressed here. We explain some theory that has been developed to cope with such situations and provide examples from practice where unavailable information is not the result of bad data handling but an inevitable phenomenon.}, language = {en} } @misc{FuegenschuhGeisslerGollmeretal., author = {F{\"u}genschuh, Armin and Geißler, Bj{\"o}rn and Gollmer, Ralf and Hayn, Christine and Henrion, Rene and Hiller, Benjamin and Humpola, Jesco and Koch, Thorsten and Lehmann, Thomas and Martin, Alexander and Mirkov, Radoslava and Morsi, Antonio and R{\"o}misch, Werner and R{\"o}vekamp, Jessica and Schewe, Lars and Schmidt, Martin and Schultz, R{\"u}diger and Schwarz, Robert and Schweiger, Jonas and Stangl, Claudia and Steinbach, Marc and Willert, Bernhard}, title = {Mathematical Optimization for Challenging Network Planning Problems in Unbundled Liberalized Gas Markets}, issn = {1438-0064}, doi = {10.1007/s12667-013-0099-8}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-17821}, abstract = {The recently imposed new gas market liberalization rules in Germany lead to a change of business of gas network operators. While previously network operator and gas vendor where united, they were forced to split up into independent companies. The network has to be open to any other gas trader at the same conditions, and free network capacities have to be identified and publicly offered in a non-discriminatory way. We show that these new paradigms lead to new and challenging mathematical optimization problems. In order to solve them and to provide meaningful results for practice, all aspects of the underlying problems, such as combinatorics, stochasticity, uncertainty, and nonlinearity, have to be addressed. With such special-tailored solvers, free network capacities and topological network extensions can, for instance, be determined.}, language = {en} } @misc{FuegenschuhHillerHumpolaetal., author = {F{\"u}genschuh, Armin and Hiller, Benjamin and Humpola, Jesco and Koch, Thorsten and Lehmann, Thomas and Schwarz, Robert and Schweiger, Jonas and Szab{\´o}, J{\´a}cint}, title = {Gas Network Topology Optimization for Upcoming Market Requirements}, doi = {10.1109/EEM.2011.5953035}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-12348}, number = {11-09}, abstract = {Gas distribution networks are complex structures that consist of passive pipes, and active, controllable elements such as valves and compressors. Controlling such network means to find a suitable setting for all active components such that a nominated amount of gas can be transmitted from entries to exits through the network, without violating physical or operational constraints. The control of a large-scale gas network is a challenging task from a practical point of view. In most companies the actual controlling process is supported by means of computer software that is able to simulate the flow of the gas. However, the active settings have to be set manually within such simulation software. The solution quality thus depends on the experience of a human planner. When the gas network is insufficient for the transport then topology extensions come into play. Here a set of new pipes or active elements is determined such that the extended network admits a feasible control again. The question again is how to select these extensions and where to place them such that the total extension costs are minimal. Industrial practice is again to use the same simulation software, determine extensions by experience, add them to the virtual network, and then try to find a feasible control of the active elements. The validity of this approach now depends even more on the human planner. Another weakness of this manual simulation-based approach is that it cannot establish infeasibility of a certain gas nomination, unless all settings of the active elements are tried. Moreover, it is impossible to find a cost-optimal network extension in this way. In order to overcome these shortcomings of the manual planning approach we present a new approach, rigorously based on mathematical optimization. Hereto we describe a model for finding feasible controls and then extend this model such that topology extensions can additionally and simultaneously be covered. Numerical results for real-world instances are presented and discussed.}, language = {en} } @misc{HillerKlugTuchscherer, author = {Hiller, Benjamin and Klug, Torsten and Tuchscherer, Andreas}, title = {An Exact Reoptimization Algorithm for the Scheduling of Elevator Groups}, issn = {1438-0064}, doi = {10.1007/s10696-013-9175-6}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-16485}, abstract = {The task of an elevator control is to schedule the elevators of a group such that small waiting and travel times for the passengers are obtained. We present an exact reoptimization algorithm for this problem. A reoptimization algorithm computes a new schedule for the elevator group each time a new passenger arrives. Our algorithm uses column generation techniques and is, to the best of our knowledge, the first exact reoptimization algorithms for a group of passenger elevators. To solve the column generation problem, we propose a Branch \& Bound method.}, language = {en} } @misc{HillerVredeveld, author = {Hiller, Benjamin and Vredeveld, Tjark}, title = {Stochastic dominance analysis of Online Bin Coloring algorithms}, issn = {1438-0064}, url = {http://nbn-resolving.de/urn:nbn:de:0297-zib-16502}, abstract = {This paper proposes a new method for probabilistic analysis of online algorithms. It is based on the notion of stochastic dominance. We develop the method for the online bin coloring problem introduced by Krumke et al (2008). Using methods for the stochastic comparison of Markov chains we establish the result that the performance of the online algorithm GreedyFit is stochastically better than the performance of the algorithm OneBin for any number of items processed. This result gives a more realistic picture than competitive analysis and explains the behavior observed in simulations.}, language = {en} } @inproceedings{HillerTuchscherer2008, author = {Hiller, Benjamin and Tuchscherer, Andreas}, title = {Real-Time Destination-Call Elevator Group Control on Embedded Microcontrollers}, series = {Operations Research Proceedings}, booktitle = {Operations Research Proceedings}, editor = {Kalcsics, J{\"o}rg and Nickel, Stefan}, publisher = {Springer}, pages = {357 -- 362}, year = {2008}, language = {en} } @inproceedings{HillerKrumkeSalibaetal.2009, author = {Hiller, Benjamin and Krumke, Sven and Saliba, Sleman and Tuchscherer, Andreas}, title = {Randomized Online Algorithms for Dynamic Multi-Period Routing Problems}, series = {Proceedings of MAPSP}, booktitle = {Proceedings of MAPSP}, pages = {71 -- 73}, year = {2009}, language = {en} }